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N AIAA-90-2354

N UNSTEADY ANALYSIS OF HOT STREAKN MIGRATION IN A TURBINE STAGE

Daniel J. Dorney, Roger L. Davis and David E. EdwardsUnited Technologies Research Center< East Hartford, DT C

'-I " ECTENateri K. MadavanNASA Ames Research Center 9AUG 1#1990Moffett, CA qOr±Ignal contnins o1 Cr-

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D ON STATZMEM Approved tg public reease AIAASAEIASMEIASEE

26th Joint Propulsion ConferenceJuly 16-18, 1990/Orlando, FL

For pernission to copy or republish, contact the American Institute of Aeronautics and Astronautics370 L'Enfant promenade, S.W., Washington, D.C. 20024

0> 0)9

Unsteady Analysis of Hot Streak Migration in a Turbine Stage

Daniel J. Dorney*Roger L. Davist

David E. Edwardst

United Technologies Research CenterEast Hartford, CT

andNateri K. Madavan §

NASA Ames Research CenterMoffett Field, CA

Abstract Nomenclature

a - Speed of soundJe - Specific energyExperimental data taken from gas turbine engines has et - Total energy

shown that hot streaks exiting combustors can have a M - Mach number

significant impact upon the secondary flow and wall P - Static pressuretemperature of the first stage turbine rotor. Under- Pr - Prandtl numberstanding the secondary flow and heat transfer effects PT - Stagnation pressuredue to combustor hot streaks is essential to turbine Re - Free stream inlet reference Reynolds numberdesigners attempting to optimize turbine cooling sys- T - Static temperaturetems. A numerical investigation is presented which ad- u - x component of velocitydresses the issues of multi-blade count ratio and three- U - Rotor velocitydimensionality effects on the prediction of combustor v - y component of velocityhot streak migration in a turbine stage> The two- and w - z component of velocitythree-dimensional Navier-Stokes analyses developed by Ic - thermal conductivityRai ef al are used to predict unsteady viscous rotor- A - Second coefficient of viscositystator interacting flow in the presence of a combus- p - First coefficient of viscositytor hot streak. Predicted results are presented for p - D ensiya two-dimensional 3-stator/4-rotor, a two-dimensional p - DensityT - Shear stress1-stator/1-rotor, and a three-dimensional 1-stator/1- 0 - Rotor rotational speedrotor simulation of hot streak migration through a tur-bine stage. Comparison of these results with experi-mental data demonstrates the capability of the three-dimensional procedure to capture most of the flow Subscriptsphysics associated with hot streak migration includingthe effects of combustor hot streaks on turbine rotor HS - Hot streaksurface temppratures."' -.~~~~~ ~~~ -". ' 5 -, ,, ,,. -. i-Inviscid

': ', J', -, ,, ,- Laminar quantity*Assistant Research Engineer, Theoretical & ComputationalIt - Stagnation quantity

Fluid Dynamics Group, Member AIAA T - Turbulent quantitytSenior Research Engineer, Theoretical & Computational - Viscous

Fluid Dynamics Group, Member AIAA . -$Senior Research Engineer, Physical & Mathematical Model- , y, z - First derivative with respect to x, y or z

ing Group, Member AIAA xx, yy, zz - Second derivative with respect to x, y or z§Principal Analyst, Sterling Federal Systems, Member AIAA 1 - Inlet quantityCopyright ©)American Institute of Aeronautics and Astro- 2 - Exit quantity

nautics, Inc., 1990. All rights reserved.

Introduction can be useful for both increasing the understanding of

this phenomena as well as to guide engineers for fu-

The drive toward low fuel consumption and maxi- ture experimental investigations. The focus of the cur-mum gas turbine efficiency for commercial aircraft has rent effort has been to perform both two- and three-

led to increases in combustor exit temperature which in dimensional rotor/stator interaction numerical simula-turn has had a direct impact on the durability of first tions which include the effects of combustor hot streaksstage turbine airfoils. In order to keep turbine airfoil in order to provide additional insight into the hot streakwall temperatures below critical levels, complex inter- migration phenomena.

nal cooling schemes are designed to lay a film of rela-tively cool air adjacent to the blade. This film cooling In the present investigation, the two- and three-

air acts as a sealant to keep the high temperature com- dimensional unsteady Navier-Stokes analyses of Rai

bustor flow from coming in direct contact with turbine et al [3,4] are used to predict the effects of a corn-

airfoil surfaces. During the design of the first stage tur- bustor hot streak on the flow in the first stage of

bine, flow field analyses which assume a uniform turbine a turbine. Two-dimensional simulations, including 3-

inlet temperature profile are used to predict airfoil sur- stator/4-rotor and 1-stator/1-rotor configurations, have

face temperature distributions. These wall temperature been performed to study the effects of stator/rotor blade

distributions are subsequently used to guide the design count on the time-averaged rotor surface mid-span tem-

of internal cooling schemes in terms of defining cooling perature distribution. In addition, to determine the

mass flow requirements and its distribution, three-dimensional effects of the hot streak migrationon the secondary flow and rotor surface temperature

Experimental data taken from actual gas turbine distribution, a three-dimensional -stator/1-rotor/1-hotcombustors, however, indicate that the flow exiting the streak simulation has been performed. The results fromcombustor has both circumferential and radial tempera- these computations have been compared to the experi-ture gradients. These temperature gradients arise from mental data reported by Butler et al [1] and the compu-the combination of the combustor core flow with the tations performed by Rai and Dring [2], Krouthen andcombustor bypass and combustor surface cooling flows. Giles [5], and Takahashi and Ni [6,7]. These numericalIt has been shown both experimentally and numeri- results and their comparison with the available exper-cally [1,2] that temperature gradients, in the absence imental data sheds new insight into the phenomena ofof total pressure non-uniformities, do not alter the flow hot streak migration and its effect on first stage turbinewithin the first stage turbine stator but do have signifi- aerodynamics and heat transfer.cant impact on the secondary flow and wall temperatureof the first stage rotor. Combustor hot streaks, whichcan typically have temperatures twice the free streamstagnation temperature, increase the extent of the sec- Numerical Integration Procedureondary flow in the first stage rotor and significantly alterthe rotor surface temperature distribution. A combus-tor hot streak such as this has a greater streamwise ve- The governing equations considered in this study are

locity than the surrounding fluid and therefore a larger the time dependent, three-dimensional Navier-Stokes

positive incidence angle to the rotor as compared to equations:

the free stream. Due to this rotor incidence variationthrough the hot streak and the slow convection speedon the pressure side of the rotor, the hot streak accu-mulates on the rotor pressure surface creating a "hot U +(F+F )r+(G,+G +(H,+Ht)z =0 (1)spot".

Both the secondary flow and wall temperature shift- whereing effects due to combustor hot streaks are importantphenomena which should be accounted for by turbinedesigners to increase turbine aerodynamic performanceand optimize turbine cooling flow schemes. Withoutproperly accounting for non-uniformities in turbine inlet .. .. Ptemperature profiles such as those related to combustor PU

hot streaks, first stage turbine performance and dura- U pV (2)

bility could suffer. Computational fluid dynamic sim- Pwulations of hot streak migration in turbine stage flows et

STATEMENT "A" Per Raymond Shreeve istNaval Postgraduate School/AAsf .Monterey, CA 93943-5000TELECON 8/13/90 VG "' _

terms are retained in the direction normal to the hub

r U 0 surface (z direction) and in the direction normal to theI PU O' blade surface (y direction). To extend the equations of

pu2 + P r( motion to turbulent flows, an eddy viscosity formula-F = puv F = - r(3) tion is used. Thus, the effective viscosity and effective

Puw ]Z thermal conductivity can be defined as:(et + P)u 7*r j

P 1 A P PL+ PT

PU 7. .C = PL + T (7)Gi= pv 2 + P Gv ryy (4) Cp PrL PrTI PVW 7 I

(et + P)v jJ The turbulent viscosity, PT, is calculated using theBaldwin-Lomax [8] algebraic turbulence model as ap-plied by Hung and Buning [9] for three-dimensionalflows.

puw TZ The numerical procedure for the three-dimensionalHi = pvw Hv= - r (5) analysis consists of a time marching, implicit, third-

pw 2 +P . order spatially accurate, upwind, finite difference(et + P)w J Th j scheme. The inviscid fluxes are discretized using a com-

bination of central, forward, and backward differences

where depending on the local eigenvalues of the flux Jaco-bians according to the scheme developed by Roe [10].The viscous fluxes are calculated using standard cen-tral differences. The alternate direction, approximate-factorization technique of Beam and Warming [11] is

r, = 2pu + A (u, + v1 + wj) used to compute the time rate changes in the primaryr~y = p (u + v.) variables. An inner Newton iteration can be used to in-

rT2 Z = p (uZ + w) crease stability and reduce linearization errors. For allcases investigated in this study, three Newton iterations

= were performed at each time step. The numerical pro-

ry = 2pv,, + A (u, + V1 + W,) cedure used for the two-dimensional analysis is similar

ry = p (vZ + wy) to that used in the three-dimensional analysis, except

T2X = rXZ (6) that the inviscid fluxes are discretized according to thescheme developed by Osher [12]. Further details of the

r,, = 2 + ( + two- and three-dimensional numerical techniques can be

rh = 2pw2 + A (uV + 1 + v+ w2 ) found in Refs. [2,3,4].Thz = uT:: + vTry + wrz + 7PPr-le:

Ty = uruy + vryy + wry + 7pPr-ley Grid Generation and Geometryrhz = Urzx + Vrzy + Wz + 7pPr ez

e P The three-dimensional Navier-Stokes analysis devel-(P Of - 1)) oped by Rai el al [2,3,4] uses five zonal grids to discretize

p (u2 + v2 + w 2) the rotor-stator flow field and facilitate relative motion= pe + 2 of the rotor. A combination of 0- and H-grid sections

are generated at constant radial spanwise locations in

For the present application, the second coefficient the blade-to-blade direction extending upstream of the

of viscosity is calculated using Stokes' hypothesis, stator leading edge to downstream of the rotor trailing

A = -2/3p. The equations of motion are completed by edge. Algebraically generated H-grids are used in the

the perfect gas law. regions upstream of the leading edge, downstream ofthe trailing edge and in the inter-blade region. The 0-

The viscous fluxes are simplified by incorporating the grids, which are body-fitted to the surfaces of the air-thin layer assumption [8]. In the current study, viscous foils and generated using an elliptic equation solution

3

procedure, are used to properly resolve the viscous flow the use of more than one Newton iteration. The zonalin the blade passages and to easily apply the algebraic boundary conditions are non-conservative, but for sub-turbulence model. Computational grid lines within the sonic flow this should not affect the accuracy of the finalO-grids are stretched in the blade-normal direction with flow solution. Further information describing the imple-a fine grid spacing at the wall. The combined H- and mentation of the boundary conditions can be found in0- overlaid grid sections are stretched in the spanwise Refs. [2,3,4,13].direction away from the hub and tip regions with a finegrid spacing located adjacent to the hub and tip. AnO-grid structure is used in the region between the ro- Resultstor blade and the tip endwall in the tip clearance region.Grid generation for the two-dimensional analysis is sim-ilar to that for the three-dimensional procedure except A numerical investigation of hot streak migration

that the O-grids are patched, rather than overlaid, into has been conducted in which predicted results using

the H-grids. the two- and three-dimensional versions of the currentNavier-Stokes procedure (ROTOR2, ROTOR3) havebeen compared with experimental data reported by

Boundary Conditions Butler et al [1]. The turbine airfoil geometry used inboth the two- and three-dimensional analyses consistsof the first stage of the UTRC Large Scale Rotating Rig

The theory of characteristics is used to determine the (LSRR) [1,14] which includes 22 stator airfoils and 28boundary conditions at the stator inlet and rotor exit. rotor airfoils. An accurate simulation of this configura-For subsonic inlet flow, the total pressure, v and w tion requires at least 11 stator and 14 rotor airfoils. Forvelocity components and the downstream runiang Rie- the 1-stator/1-rotor two- and three-dimensional simu-mann invariant, R1 = u + .Y,, are specified while the lations, the rescaling strategy of Madavan et al [15] isupstream running Riemann invariant, R2 = U - -"-1, used to reduce the number of airfoils to one stator andis extrapolated from the interior of the computational one rotor. The stator was scaled down by a factor ofdomain. Inlet flow boundary conditions within the (22/28) and it was assumed that there were 28 statorhot streak region are updated using Riemann invari- airfoils. The pitch to chord ratio of the stator was notants where the velocity and speed of sound reflect the changed. This is different than the scaling strategy usedstatic and stagnation temperature increase in the hot by Rai and Dring [2] in which the rotor was scaled bystreak. The static and total pressure in the hot streak a factor of (28/22) and it was assumed there were 22is assumed to be equal to that of the undisturbed inlet rotor airfoils. For the two-dimensional 3-stator/4-rotorflow. For subsonic outflow the pressure ratio P2/Ptl is simulation, a rescaling strategy was used to reduce thespecified while the v and w velocity components, en- number of airfoils to 3 stators and 4 rotors. In this casetropy, and the downstream running Riemann invariant it was assumed that there were 21 stator airfoils and 28are extrapolated from the interior of the computational rotor airfoils and the stators were enlarged by the factordomain. Absolute no-slip boundary conditions are en- (22/21).forced at the hub and tip endwalls of the stator region,along the surface of the stator, and along the outer cas- In the experimental study [1], one hot streak wasing (tip endwall) of the rotor. Relative no-slip bound- introduced through a circular pipe at 40% span, andary conditions are imposed at the hub and along the midway between, two stator airfoils of the LSRR. The

surface of the rotor. Periodicity is enforced along the temperature of the hot streak was twice that of the sur-

outer boundaries of the H-grids in the circumferential rounding inlet flow, whereas th, hot streak static and

(0) direction. In the present, study the flow is assumed stagnation pressures were identical to the free stream.to be adiabatic. The hot streak was seeded with CO2 and the path of

the hot streak determined by measuring CO2 concen-Dirichlet conditions, in which the time rate change in trations at various locations within the turbine stage.

the vector U of Eq. (2) is set to zero, are imposed at In the two-dimensional 1-stator/1-rotor simulation andthe grid interface boundaries located between the stator three-dimensional I-stator/ 1-rotor simulation, one hotand rotor H-grids and at the overlaid boundaries of the streak is introduced to the inlet of each stator pas-0- and H-grids in the stator and rotor regions. The flow -sage. -For the- two-dimensional 3-stator/4-rotor simu-variables of U at zonal boundaries are explicity updated lation, one hot streak is introduced to the inlet of everyafter each time step by interpolating values from the ad- third stator passage. The temperature of the hot streakjacent grid. Because of the explicit application of the in the current investigation is 1.2 times the temperaturezonal boundary conditions, large time steps necessitate of the surrounding inlet flow. For the two-dimensional

4

3-stator/4-rotor simulation, the hot streak was intro- each of the three stator grids was constructed with 101 xduced over a distance equal to one quarter of a stator 31 (streamwise x tangential) grid points in the O-gridpitch and centered at the mid-gap position between the and 71 x 51 grid points in the H-grid. Each of the foursecond and third stator. For the two-dimensional 1- rotor grids was constructed with 101 x 31 grid points instator/1-rotor simulation, the hot streak was introduced the O-grid and 75 x 51 grid points in the H-grid. A totalover one quarter of the stator pitch and centered at mid- of 48,080 grid points and an average blade wall spacinggap. In the three-dimensional simulation, the hot streak of 2.0x 10-' inches were used in this simulation. For thewas introduced through a two inch diameter circular re- two-dimensional 1-stator/1-rotor simulation, the statorgion which corresponds to the two inch diameter pipe zone was constructed with 101 x 31 grid points in the 0-used in the experiment [1]. The center of the hot streak grid and 75x 31 grid points in the H-grid. The rotor zonewas located at the mid-gap, 40% span location. In both was constructed with 101 x 31 grid points in the O-gridthe two- and three-dimensional calculations, the tem- and 71 x 31 grid points in the H-grid. A total of 10,788perature profile used at the stator inlet to simulate the grid points and an average wall spacing of 2.0 x 10-4

combustor hot streak consisted of a hyperbolic tangent inches were used in this calculation. Examples of the(step-like) distribution, grid topology used in the two-dimensional simulations

are shown in Refs. [2,4].A 15% axial gap between the stator and rotor was

used in both the two-dimensional and three-dimensional Results of the two-dimensional simulations havesimulations, while the experimental configuration had a been compared with the time-averaged experimental65% axial gap. It has been demonstrated [16] that the data [1,14]. Figure 1 shows a comparison of the time-axial gap has no significant impact on either the time- averaged stator surface pressure distribution predictedaveraged pressure distributions or time-averaged heat by the numerical analysis for the 3-stator/4-rotor andtransfer coefficients on the stator or rotor. Secondary 1-stator/1-rotor configurations with experimental dataflow and other viscous mechanisms, however, can be reported by Dring ef al [14]. The time-averaged pres-affected by the stator/rotor axial gap. The inlet Mach sure coefficient is defined as:number to the stator was 0.07 and the inlet flow wasassumed to be axial. The rotor rotational speed was410 rpm. The experimental flow coefficient was =- = Pavg- Pt(u/U = .68, while the numerical simulations held a flow = pU 2 (8)coefficient of 0 = .78. The free stream Reynolds numberwas 100,000 per inch. A pressure ratio of P2/Pt = 1

.963 was determined from the inlet total pressure and where Pavg i the local time-averaged pressure, Pt1 isthe static pressure measured in the rotor trailing-edge the inlet total pressure, P, is the average inlet freeplane. stream density, and U is the rotor velocity. The pre-

dicted results for the 3-stator/4-rotor and 1-stator/1-rotor configurations both exhibit good agreement with

Two-Dimensional Simulations the experimental data. Figure 2 presents a compari-son of the predicted results of the two simulations with

A two-dimensional 3-stator/4-rotor and a 1-stat,/1- the experimental time-averaged surface pressure datarotor hot streak simulation have been performed as for the rotor. Excellent agreement exists between thepart of a numerical investigation into the effects of sta- numerical predictions and the data. The predicted re-tor to rotor blade count on hot streak migration and sults shown in Figs. 1 and 2 are also in good agreementtime-averaged wall temperature distributions. The two- with those reported by Rai et al [2,4] for a similardimensional calculations performed during this investi- 1-stator/1-rotor configuration with and without a hotgation were computed on a four processor Alliant FX- streak. These figures substantiate that the effect of the80 mini-supercomputer. Typical calculations required hot streak on the time-averaged pressure fields of the.00191 seconds per grid point per iteration computation stator and rotor is negligible since the static and stag-time. For both two-dimensional simulations, approxi- nation pressure of the hot streak is identical to that ofmately six cycles at 3000 iterations per global cycle were the free stream.needed to obtain a time-periodic solution. A global cy-cle orrsponstothe oto blde rtatngtrouhan.... A measure of the unsteadiness of the flow can be ob-cle corresponds to the rotor blade rotating through-anangle of 2x/N where N is the number of stator blades tained by evaluating the size of the surface pressure flu-(i.e. N=3 and N--l). cuations of the stator and rotor. The pressure fluctua-tions can be quantified through the use of an unsteady

For the two-dimensional 3-stator/4-rotor simulation, pressure amplitude coefficient defined by:

5

1.0 3.60A- EXP DATA 0 = .78 [13] A- EXP DATA 0 = .78 [13]- 3-STATOR/4-ROTOR 0 =.76 3-STATOR/4-ROTOR 0 = .78- - 1-STATOR/1-ROTOR 0 =.78 --- I-STATOR/1-ROTOR 0 = .78

-2.0 2.40Cp C,

/'

-5.0 1.20 /

,--4-6L PRESSURE SIDE

SUCTION SIDE ATRAILING EDGE-8.0 , 0.00 , , I 1

-7.0 -5.o -3.0 -1.0 1.0 -8.0 -4.0 0.0 4.0 8.0

x x

Figure 1: Predicted and experimental blade loading for Figure 3: Pressure amplitude coefficient distribution forthe stator (2-D) stator (2-D)

-I.0 3.60A- EXP DATA0 = .78 [13] A -EXP DATA 0 =.76 [13]

3-STATOR/4-ROTOR 0 = .78 3STATOR/4-ROTOR = .78-STATOR/4-ROTOR 0=.8--- I-STATOR/1-ROT )R 0 = .78- - I-STATOR/I-ROTOR = .78

-4.0- 2.40-

Cp (5,/

-7.0- 1.20 A\ \

A LEADING EDGE

-10.0 0 ,40.00 SUCTION SIDE PRESSURE SIDE

0.0 2.0 4.0 6.0 8.0 -8.0 -4.0 0.0 4'.0 8.0x x

Figure 2: Predicted and experimental blade loading for Figure 4: Pressure amplitude coefficient distribution forthe rotor (2-D) rotor (2-D)

experimental data. This figure shows that the ampli-

e Pmaz - Pmin tude of the pressure variations is small on the stator ex-IPiU2 (9) cept near the trailing edge. The predicted results for the

1-stator/1-rotor configuration show larger pressure fluc-

....... . tuations than for the 3-stator/4-rotor configuration andFigure 3 illustrates the predicted and experimental the experimental data. The larger fluctuations are due

values of the unsteady pressure amplitude coefficient to pressure signals which do not decay for even bladefor the surface of the stator. Good agreement exists count configurations [4] and the reflective exit bound-between the predicted 3-stator/4-rotor results and the ary conditions used in the numerical procedure. Fig-

6

ure 4 illustrates the predicted and experimental values to be caused soley by the relative inlet angle differenceof the unsteady pressure amplitude coefficient for the between the hot streak and the surrounding fluid atrotor. Good agreement exists between the predicted 3- the inlet to the rotor passage [1]. Results of the two-stator/4-rotor results and the experimental data except dimensional simulation confirm experimental observa-near the pressure surface trailing edge, where the pres- tions which indicate that the static pressure, total pres-sure variations are greater than those observed experi- sure, and absolute flow angle are the same in the hotmentally. Again, the predicted pressure fluctuations for streak as in the surrounding fluid at the stator exit.the 1-stator/1-rotor configuration are larger than those The difference in the total temperature between the hotpredicted in the 3-stator/4-rotor configuration as well streak and the surrounding fluid results in an absoluteas the experimental data. Figures 1-4 illustrate that velocity difference equal to the square root of the ratiothe stator/rotor blade count ratio has little effect on of the hot streak and surrounding fluid temperatures. Inthe time-averaged pressure field, but has considerable the relative frame, a difference in the rotor relative inletimpact on the unsteady pressure field. angle and velocity results. As a result, the hot streak

fluid moves towards the pressure surface at a higherFigure 5 shows the predicted 3-stator/4-rotor andrelative velocity compared to the surrounding fluid [1].

1-stator/1-rotor time-averaged temperature coefficient Time-averaged static temperature contours for the rotordistributions compared with the experimental data re- passage of the two-dimensional 3-stator/4-rotor config-ported by Butler et al [1] for the rotor. Also included in uration are shown in Fig. 6. Although the hot streakFig. 5 are the two-dimensional numerical results of Rai fluid accumulates near the pressure side of the rotor,and Dring [2] and Krouthen and Giles (rescaled) [5]. the hot fluid does not penetrate the boundary layer toThe temperature coefficient, CT, is defined as [2,7]: the surface of the rotor blade. The thin layer of cooler

fluid which exists between the hot fluid and rotor pres-sure surface helps explain the flat temperature coeffi-

S T- T, cient profiles shown in Fig. 5 for the two-dimensionalCT'- (10) solutions.CT=Tagrie - TI

where T is the time-averaged local temperature andTagrle is the time-averaged mid-span temperature at All of the two-dimensional numerical simulationsthe rotor leading edge. This definition of the tem- shown in Fig. 5 predict nearly equal time-averaged tem-perature coefficient facilitates comparison between the peratures on the pressure and suction surfaces and failpresent solutions and the predicted results of Rai and to predict the increased rotor pressure surface tem-Dring [2], Krouthen and Giles [5], and the experimen- peratures observed experimentally. Clearly, an addi-tal data [1]. The time-averaged temperature coefficient tional mechanism other than the rotor incidence vari-distribution for the 1-stator/1-rotor hot streak calcula- ation through the hot streak is accounting for the ex-tion is essentially the same as that reported by Rai and perimentally observed temperature rise on the pressureDring [2] except for a small difference on the pressure side of the airfoil.surface. The discrepancies on the pressure surface areprobably due to the difference in airfoil scaling strate-gies discussed eariler. The predicted time-averaged tem-perature coefficient distribution for the pressure surface toin ettrbinsight it t eune pheoof te 3staor/-roor imuatin i siila totha ofwithin the turbine stage, animated sequences of the flowof the 3-stator/4-rotor simulation is similar to thatf field were created. Figure 7 shows the temperature fieldthe -stator/1-rotor calculat bution s s rfie at one instant in time during the animated sequence.temperature coefficient distribution shows lower time- hot streak is undisturbed as it migrates throughaveraged tem peratures than that predicted in the - t e s a o a s g , e c p h t t e w d h o h ostator/1-rotor calculation. The lower suction surface tesao asgecp httewdho h oalclaion The ltrsction sua-e streak decreases due to flow acceleration. The geometrytemperatures predicted inof the turbine rotor blades is such that the hot streaktionhemayrbentheoresultaofsintroducingatoneehottstreaktion may be the result of introducing one hot streak impinges first on the suction surface, then wraps aroundevery third stator passage instead of a hot streak in the leading edge and moves along the pressure surface.each stator passage. TheAs a result of this movement, the rotor pressure surfacebution obtained by Krouthen and Giles-J5] is similar to temperature does not peak until some time after thethe present 3-stator/4-rotor prediction. rotor blade interacts with the hot streak. The hot streak

The segregation of the hot gases to the pressure side assumes a V shape as it continues to convect throughof the rotor passage has been, until this time, believed the rotor passage.

7

2.50 - EXP DATA 0 = .68 [I]

3-STATOR/4-ROTOR.. -- I-STATOR/1-ROTOR.... KROUTHEN AND GILES [5] A

..... RAI AND DRING [2] AALL CALCULATIONS - 0 = .78

1.50

050T A :

A

SUCTION LEADING PRESSURESIDE EDGE SIDE

-0 50 r ,I-4.0 2.0 8.0 14.0 20.0s

Figure 5: Predicted and experimental time-averagedsurface temperature for rotor (2-D)

Figure 7: Static temperature contours for 2-D hot streak

gration effects on the time-averaged rotor surface tem-perature distribution. The three-dimensional calcula-tion was performed on the NAS Cray 2 supercomputerlocated at the NASA Ames Research Center. This cal-culation required .000263 seconds per grid point per it-eration computation time. Seven cycles at 2000 itera-tions per cycle were needed to obtain a time-periodicsolution.

For the three-dimensional simulation, the stator gridsystem was constructed with 101 x 21 grid points ineach spanwise 0-grid and 58 x 31 grid points in eachspanwise H-grid. The rotor grid system was constructedwith 101 x 21 grid points in each spanwise 0-grid and60 x 31 grid points in each spanwise H-grid. A totalof 51 0-H grid planes were distributed in the spanwisedirection. The rotor region had a tip clearance gridsystem that contained 101 x 11 grid points in each of7 spanwise locations. A total of 410,677 grid points

Figure 6: Time averaged static temperature contours were used in the three-dimensional simulation. A wallfor 2-D hot streak (3-stator/4-rotor) spacing of 5.0 x 10- 4 inches was used in the blade-to-

blade direction, while a wall spacing of 3.0 x 10-2 incheswas used in the spanwise direction. The experimental

Three-Dimensional Simulation rotor has a tip gap equal to 1% of the rotor span, whilethe tip clearance in the three-dimensional simulation isequal to 3.9% of the rotor span. Illustrations of the

A 1-stator/1-rotor three-dimensional hot streak simu- three-dimensional computational grid topology can belation with a hot streak temperature 20 percent greater found in Refs. (3,15].than the free stream temperature has also been per-formed to establish the three-dimensional hot streak mi- As part of the numerical investigation, the predicted

8

o - EXP DATA 0 = .78 (131- I-STATOR/I-ROTOR = o EXP DATA - .778[13

98%- I-STATOR/I-ROTOR 4 = .78

1.0%

87.5%87.5%

75%

-2.0

-5.0%

25%-

25%

12.5%51.0 - 1 2. 5%

-2.0 20 0 . -4"O"-50.

-7.0

-8.0--6.00 -4.50 - 1. f50 o.o

X 0.0 2.0 4.0 6.0 80X

Figure 8: Time-averaged pressure coefficient distribu-tion for stator Figure 9: Time-averaged pressure coefficient distribu-

tion for rotor

unsteady pressures and temperatures have been time-averaged and compared to the experimental data [14].Figure 8 illustrates the predicted and experimental the mid-span section of the stator. The predicted suc-time-averaged pressure coefficient distributions on the tion surface pressure fluctuations near the trailing edgestator at 2, 12.5, 25, 50, 75, 87.5 and 98% span loca- are smaller than those of the experimental data and thetions. In general, there is good agreement between the two-dimensional results shown in Fig. 3. In addition,

tion. I geera, thre s god greeentbeteenthethe pressure amplitude coefficient on the pressure sur-predicted results and the experimental data. The pre-thprsuea lidecfiintotepesreu-dicted results also agree well with those presented by face does not rise near the trailing edge compared toRai [3] and Madavan e a! [15]. the experimental data and predicted two-dimensionalresults (Fig. 3). Figure 11 illustrates the predicted andPredicted and experimental time-averaged pressure experimental values of the unsteady pressure amplitude

coefficient distributions for the rotor at the 2, 12.5, coefficient for the mid-span section of the rotor. Fair25, 50, 75, 87.5 and 98% span locations are shown in agreement exists between the predicted results and ex-Fig. 9. Good agreement between the predicted results perimental data as the predicted results show largerand the experimental data is observed from the hub to pressure fluctuations than those observed experimen-the mid-span location of the rotor. Some discrepancies tally and predicted two-dimensionally (Fig. 4). Thebetween the predicted and the experimental pressure stator and rotor pressure amplitude results shown indistributions are evident on the suction surface of the Figs. 10 and 11 are similar to the coarse grid predic-rotor, however, from the mid-span location out to the tions of Rai [3]. Madavan et al [15] showed that thetip. These discrepancies are probably caused by the pressure amplitudes on both the stator and rotor arestronger secondary flows which arose in the calculation sensitive to the computational grid density. The resultsdue to the relatively large tip clearance, shown in Figs. 10 and 11 are predicted using the same

fine computational grid density as Madavanet al [15].Figure 10 shows the predicted and experimental val- However, the wall spacing used in the current calcula-

ues of the unsteady pressure amplitude coefficient for tion was increased in order to yield a unif, rm grid near

9

3.00 300"3. - EXP DATA0 = 781 A - EXP DATA , = .68 [1]

A 7- I-STATOR/I-ROTOR 0 = 78ISTATOR/I-ROTO b = .78 ... TAKAHASHI AND NI o, = .6S 6

2.00 1.80 -AA

AA A. A

--

1.00 A0.60 AA 7'A

A

AESUCTION LEADING PRESSU E

SUCTION S DE TRAILING EDGE SIDE EDGE SIDE0.00 , ,I , -0.60 , I , ,

-6.0 -. 0 .0 .0 6.0 -4.0 20 .0 14.0 20.0

X S

Figure 10: Pressure amplitude coefficient for mid-span Figure 12: Predicted and experimental time-averaged

stator section surface temperature for rotor mid-span section

3.00 - .0

3 A0 ,-x EXP DATA € = .78 [13] 1 tribution for the mid-span section of the rotor. Also-1-STATOR/1-ROTOR € = .78 included in Fig. 12 are the three-dimensional invis-

A cid (with viscous modelling) results of Takahashi and

Ni [6,7]. The three-dimensional simulation correctly

200 predicts that the pressure surface of the rotor is sub-dr itAI ject to much higher time-averaged temperatures than

the suction surface. In addition, the present three-dimensional calculation correctly predicts the rapid fall-

A.00off in the time-averaged temperature on the suction sur-

1.00- .0

A, A face. Comparison between the current results and the

A solution of Takahashi and Ni shows that both three-dimensional techniques predict similar trends with the

A ADING ED ESUCTION SIDE * PRESSURE SIDE current Navier-Stokes technique providing more de-

-. 0 -. 0 00 4.0 .0 tailed with the data. This com-

x parison, along with the two-dimensional results, implies

that the interaction between the secondary and walllayer flows in the rotor passage and the hot streak isan important factor in the time-averaged rotor surfaceFigure 11: Pressure amplitude coefficient for mid-span temperature distribution. Furthermore, this compari-

rotor section son highihghts the importance of accurately predicting

the secondary and wall layer flows through the turbine

stage in order to correctly predict the rotor surface temr -

mid-span/mid-gap, which was necessary to maintain a perature distributions.

circular hot streak. Comparison between the current

results and those of Rsai [3] and Madavane al [15] show The predicted rotor surface temperature coefficient

that the predicted pressure amplitude is not only sensi- contours are illustrated in Fig. 13, while the experi-

tive to computational grid density, but also to the span- mental, contours [1] are shown in Fig. 14. The pre-

wise distribution of grid points. dicted contour patterns are similar to the experimen-

tal contours, except near the pressure surface trailing

Figure 12 illustrates the predicted and experimental edge where the numerical contours do not close as the

values of the time-averaged temperature coefficient dis- experimental data indicates. This difference between

10

TIP

HUB

SUCTION SURFACE L.E. PRESSURE SURFACE T.E.

Figure 13: Predicted time-averaged surface temperature contours for rotor airfoil

TIP

HUBSUCTION SURFACE L.E. PRESSURE SURFACE T.E.

Figure 14: Experimental time-averaged surface temperature contours for rotor airfoil [1]

the prediction and the experiment coincides with that tion surface of the stator blades and the pressure surface

shown in Fig. 12 for the mid-span pressure surface near of the rotor blades. This sequence of pictures illustrates

the trailing edge. This discrepancy is probably due to the migration of the hot streak through the stator pas-

the difference in flow coefficients between the simula- sage and how it is broken into discrete spherical eddies

tion (0 = .78) and the experiment (0 = .68), resulting as it interacts with the passing rotor blades. The hot

in a rotor inlet flow with 5 degrees more positive inci- fluid remains on the pressure surface of the rotor for a

dence in the simulation than in the experiment. Both long period of time after it encoun, ers the hot streak,

the numerical and experimental results illustrate that eventually migrating towards the pressure surface tip,

the hot fluid spreads over the entire pressure surface of where it leaks over onto the suction surface.

the rotor, while on the suction surface the hot fluid isgenerally confined to the mid-span region of the rotor Conclusionssurface. Experimental studies have shown that combustor hot

streaks can significantly affect the secondary flows andAs was performed for the two-dimensional simula- wall temperature of the first stage turbine rotor. To

tion, animated sequences of the flow field were created gain insight into the secondary flow and heat transferfrom results of the three-dimensional simulation. A se- effects on a first stage rotor due to a combustor hotquence from the animation of the T = 1.05 temperature streak, numerical simulations of hot streak migrationisotherm at four instants in time during a global cycle through a turbine stage have been performed. The goal

are shown in Figs. 15 and 16. These four instants in of these simulations has been to understand the physical

time correspond to 0, 25, 50 and 75% of the global cy- mechanisi.as which control the migration of hot streakscle, where the global cycle is equal to the rotor blade through a turbine stage and lead to "hot spots" on the

moving a distance equal to one stator pitch. Figure 15 rotor pressure surface.shows the isotherm from a viewing position that dis-plays the pressure surface of the stator blades and the Results have been presented for both two-dimensional

suction surface of the rotor blades. Figure 16 shows the and three-dimensional simulations of hot streak migra-

isotherm from a viewing position that displays the suc- tion through a turbine stage. The predicted results from

11

uj0

-4Z

0

E-44

i

C4N

5-

5..

005-

Q.)

5..

0

05..

5..

0

It~0

I:

I..

0 U,

the two-dimensional simulations indicate that blade Journal of Propulsion and Power Vol. 5, May-June,count ratio has little effect on predicted time-averaged 1989.surface pressure and temperature distributions, but asubstantial effect on the unsteady flow characteristics. [4] Rai, 1M. M. and Madavan, N. K., "Multi-Airfoil

subsantal efec onthe nstady lowchaacteistcs. Navier-Stokes Simulations of Turbine Rotor-StatorThese two-dimensional simulations fail to predict the naeratokes Simulain of T i R raexperimentally observed increase in time-averaged pres-sure surface temperatures due to the hot streak. Results [5] Krouthen, B., and Giles, M., "Numerical Investi-of the three-dimensional hot streak simulation, however, gation of Hot Streaks in Turbines," AIAA Paperconfirm experimental observations that high tempera- 88-3015, July, 1988.ture hot streak fluid accumulates on the pressure surfaceof the rotor blades, resulting in a high time-averaged [6] Takahashi, R. and Ni, R. H., "Unsteady Eulersurface temperature "hot spot". The inability of the Analysis of the Redistribution of an Inlet Temper-two-dimensional simulations to predict the increased ro- ature D o TA ator pressure surface temperatures underscores the im- 2262, July, 1990.portance of including three-dimensional viscous effects. [7] Sharma, 0. P., Pickett, G. F., and Ni, R. H., "As-In addition, the influence of secondary flows on the pre- sessment of Unsteady Flows in Turbines," ASMEdicted three-dimensional migration pattern of the hot Paper 90-GT-150, 1990.streak has been shown to be consistent with experimen- [8] Baldwin, B. S. and Lomax, H., "Thin-Layer Ap-tal data.[8BadiBS.ndLm ,H."Ti-yrA-

proximation and Algebraic Model for Separated

Acknowledgements Turbulent Flows," AIAA Paper 78-257, January,1978.

This work was supported by the Naval Air Sys- [9] Hung, C. M. and Buning, P. G., "Simulationtems Command under NAVAIR contract N00014-88- of Blunt-Fin-Induced Shock-Wave and Turbulent-0677 from the office of George Derderian with Ray- Layer Interaction," Journal of Fluid Mechanzcs,mond Shreeve of the Naval Post Graduate School acting Vol. 154, pp.163-185, 1985.as technical monitor and the United Technologies Re-search Center under the Corporate Research Program. [10] Roe, P. L., "Approximate Riemann Solvers, Pa-The authors would like to thank Man Mohan Rai and rameter Vectors, and Difference Schemes," Jour-Linda Haines of the NASA Ames Research Center for nal of Computational Physics, Vol. 43, pp.357-372,assistance in computational aspects of this investiga- 1981.tion. The authors appreciate the helpful discussions [11] Beam, R. M. and Warming, R. F., "An Implicitwith Robert Dring and Dave Joslyn of the United Tech- [11)oBe R. an r R. F., " A icitnoloiesResarc Ceterand m Sarm, Rn Tka- Factored Scheme for the Compressible Navier-nologies Research Center and Om Sharma, Ron Taka- Stokes Equations," AIAA Paper 77-645, 1977.hashi, and Bob Ni of Pratt & Whitney concerning inter-pretion of the experimental results. The authors would [12] Chakravarthy, S. and Osher, S., "Numerical Ex-also like to thank Diane Rodimon of the United Tech- periments with the Osher Upwind Scheme for thenologies Research Center for help with the graphic vi- Euler Equations," AIAA Paper 82-0975, 1982.sualization. [13] Rai, M. M., "An Implicit, Conservative, Zonal-

References Boundary Scheme for Euler Equation Calcula-tions," AIAA Paper 85-0488, 1985.

[1] Butler, T. L., Sharma, 0. P., Joslyn, H. D., and [14] Dring, R. P., Joslyn, H. D., Hardin, L. W., andDring, R. P., "Redistribution of an Inlet Temper- Wagner, J. H., "Turbine Rotor-Stator Interaction,"ature Distortion in an Axial Flow Turbine Stage," Journal of Engineering for Power, Vol. 104, Octo-Journal of Propulsion and Power, Vol. 5, January- ber, 1982.February, 1989. [15] Madavan, N. K., Rai, M. M., and Gavali, S., "Grid

[2] Rai, M. M. and Dring, R. P., "Navier-Stokes Analy- Refinement Studies of Turbine Rotor-Stator Inter-ses of the Redistribution of Inlet Temperature Dis- action," AIAA Paper 89-0325, 1989.

tortions in a Turbine," Journal of Propulsion and [16] Joslyn- H. D. and Dring, R. P, "Three DimensionalPower, Vol. 6, May-June 1990. Flow and Temperature Profile Attenuation in an

Axial IFlow Turbine," UTRC Report R89-957334-[3] Rai, M. M., "Three-Dimensional Navier-Stokes 1, March, 1989.

Simulations of Turbine Rotor-Stator Interaction,"

14